mesh inflations modeling and calculations with units

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Permalink Reply by Daniel Piker on November 5, 2012 at 7:51am

See my recent post here for some info on the units in Kangaroo:

http://www.grasshopper3d.com/group/kangaroo/forum/topics/units-mass...

The PressureLevel input is your pressure in Pa divided by 6.

(To explain this odd division factor : I calculate the pressure force from the cross-product of 2 of the triangle's edge vectors. This gives a vector in the direction normal to the triangle, and of magnitude equal to the area of the parallelogram formed by those edges. So it has to be divided by 2 to get the area of the triangle, and by 3 to get the force per vertex. I just wasn't thinking about units when I added that force, so neglected to include this factor, but will fix that in the next version)

For the proper numerical values of membrane stiffness you'll actually need the new membrane element, which isn't in the current release of Kangaroo, but will be in the next release.

Permalink Reply by MGuin on November 6, 2012 at 7:30am

Thank you Daniel! I didn't know this :) So I'm working in metres, therefore pascals, newtons, etc.

I have a follow-up question, if you don't mind...

I understood perfectly your explanation on the pressure level imput, and how to relate this with my pressure value in Pa. However, I don't know how to make the conversion for finding a value for the stiffness of the springs in my triangulated mesh, in a way that would relate to the material properties of the membrane that I want to model.

As I understand it, what kangaroo is doing is translating my mesh membrane into a triangulated grid of springs that will simulate the behaviour of this membrane as a particle system.

In my example, I'm working with a 12x12m cushion made of two square etfe membranes. I know that my etfe membrane has a tensile modulus of elasticity of 900MPa, I also know that it is 0.25mm thick. On the other hand, for the particle model, the membrane is being translated into grid of springs where the cell size is 0.5x0.5m, so I have a grid of springs of 0.5m length, and I also have shear springs that define the diagonals, each of 0.35m length. How can I translate the module of elasticity and thickness of the membrane into a value for the stiffness of these springs? Is there a formula that can help me relate these two? Should shear springs have a different stiffness than the ones forming the reticular grid?

The kangaroo model is a modification of a cushion you shared some time ago. With the pressure level and stiffness that I found in your model, I already get a nice geometry. However, I'd like to find the shape of a cushion that would have the characteristics that I mentioned previously.

I'd like to try a pressure of 300Pa, which would mean a Pressure level of 50.

I'm really excited by the possibilities that your plug-in offers. It's very fun to use, and intuitive enough for an architecture student to play with! Thanks for sharing.

Melissa

Attachments:

• 12x12m etfe cushion.3dm, 82 KB
• 12x12m etfe cushion.gh, 11 KB

Permalink Reply by Daniel Piker on November 6, 2012 at 8:41am

Hi Melissa,

This is what I mean about the new membrane element - the next release of Kangaroo will contain a new force component which calculates the force based on the geometry of a triangle, and the tensile strength of the material.

(because although one can simulate membrane structures with combinations of 1-D elements as in a pure spring-particle model, it is hard to link these to real numerical values for material properties)

Permalink Reply by ELENA CHIRIDNIK on April 3, 2015 at 9:33am

Hello, Daniel,

I am very much looking forward to the membrane element. Is it available in the recent Kangaroo 2? Or maybe there is a way to improve described above examples with a new Kangaroo release?

Permalink Reply by Daniel Piker on April 3, 2015 at 10:29am

Hi Elena,

The membrane element is included with version 0.099, and there are some examples of its use with the download.

I didn't yet rewrite this element for with the new solver in 2.0 but will do soon.

Permalink Reply by ELENA CHIRIDNIK on April 3, 2015 at 11:03am

Thank you, Daniel!

Permalink Reply by Brian Loudon on November 13, 2012 at 6:52am

Interesting point about the Pressure level! Can I ask if there is a similar issue with the Hydrostatic component?

I'm actually looking at a flexible membrane's geometry (not worried about forces at the moment) with a pressure component on one side and a hydrostatic component affecting the other side, so it's important that I understand if the units are consistent.

many thanks,

Brian

Permalink Reply by Daniel Piker on November 13, 2012 at 7:28am

The hydrostatic force component calculates the triangle area and direction for the force in exactly the same way as described above for the pressure force component. Then it multiplies by the density and depth (measured at the centre of the triangle).

So if you have a triangle with its centre at (0,0,-1), and a 'Pressure' force component acting on one side with a PressureLevel input of 1.0, and a 'Hydro' force component acting on the other side with a 'Density' input of 1.0, then the net force will be zero and it will not move.

I realized that the input I've labelled 'Density' should more properly be called 'weight density' or 'specific weight' to avoid confusion (as it does not multiply by g )

Permalink Reply by Brian Loudon on November 13, 2012 at 7:37am

Hi Daniel, thanks for responding so quickly! So, just to avoid confusion, the input should be; (in kg, m, s)

(density in kg/m3) x gravity (ms-2) / 6  

dividing by 6 as in the above case with the pressure level?

thanks again, apologies that I haven't contributed more to the forums, it's been on my todo list, was thinking that I should try and do a wee tutorial or something with what I've learned over the past months.

cheers, Brian

Permalink Reply by Daniel Piker on November 13, 2012 at 7:46am

Yes, that is correct.

(I'll get rid of this silly need for the division by 6 in the next version, and make sure all the inputs are labelled clearly with units)

That would be great if you do want to share some of your knowledge - would be interested to hear more about what you've been using it for.